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29 March 2024
 
  » arxiv » quant-ph/0505007

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A new algorithm for directed quantum search
Tathagat Tulsi ; Lov Grover ; Apoorva Patel ;
Date 2 May 2005
Subject quant-ph
AbstractQuantum searching requires precise knowledge of problem parameters (such as the fraction of target states) for efficient operation. Recently an algorithm has been discovered, referred to as the Phase-$pi/3$ search algorithm, which gets around this limitation. This algorithm can search a database with the fraction of target states equal to $1-epsilon$ so that in $q$ queries it produces a probability of error equal to $epsilon^{2q+1}$ which has since been proved to be optimal. This paper gives a different algorithm which has the same worst-case behavior as the Phase-$pi/3$ search algorithm but much better average-case behavior. Furthermore the new algorithm gives $epsilon^{2q+1}$ convergence for all integral $q$, the Phase-$pi/3$ search algorithm, requires $q$ to be $(3^{n}-1)/2$, with $n$ a positive integer. In the new algorithm, the operations are controlled in a special way by two ancilla qubits, and fixed point behavior is achieved by irreversible measurement operations.
Source arXiv, quant-ph/0505007
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